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On conditional compactly uniform pth-order integrability of random elements in Banach spaces

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  • Cabrera, Manuel Ordóñez
  • Volodin, Andrei I.

Abstract

The notion of conditional compactly uniform pth-order integrability of an array of random elements in a separable Banach space concerning an array of random variables and relative to a sequence of [sigma]-algebras is introduced and characterized. We state a conditional law for randomly weighted sums of random elements in a Banach space with the bounded approximation property, and we prove that, under the introduced condition, the problem can be reduced to a similar problem for random elements in a finite-dimensional space.

Suggested Citation

  • Cabrera, Manuel Ordóñez & Volodin, Andrei I., 2001. "On conditional compactly uniform pth-order integrability of random elements in Banach spaces," Statistics & Probability Letters, Elsevier, vol. 55(3), pages 301-309, December.
    • Handle: RePEc:eee:stapro:v:55:y:2001:i:3:p:301-309
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    References listed on IDEAS

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    1. Hu, Tien-Chung & Cabrera, Manuel Ordóñez & Volodin, Andrei I., 2001. "Convergence of randomly weighted sums of Banach space valued random elements and uniform integrability concerning the random weights," Statistics & Probability Letters, Elsevier, vol. 51(2), pages 155-164, January.
    2. Gut, Allan, 1992. "The weak law of large numbers for arrays," Statistics & Probability Letters, Elsevier, vol. 14(1), pages 49-52, May.
    3. Cuesta, Juan A. & Matrán, Carlos, 1988. "Strong convergence of weighted sums of random elements through the equivalence of sequences of distributions," Journal of Multivariate Analysis, Elsevier, vol. 25(2), pages 311-322, May.
    4. Rosalsky, Andrew & Sreehari, M., 1998. "On the limiting behavior of randomly weighted partial sums," Statistics & Probability Letters, Elsevier, vol. 40(4), pages 403-410, November.
    5. Sung, Soo Hak, 1999. "Weak law of large numbers for arrays of random variables," Statistics & Probability Letters, Elsevier, vol. 42(3), pages 293-298, April.
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